Exponent Expression Help: Understanding 0^√0 = √0⁰ and Its Truth Value

In summary, the conversation discusses the expression 0^0 and whether it is true or not. It is stated that if 0^0 is defined as undefined, then the expression does not hold. The conversation also mentions simplifying the expression using logarithms and assumptions of using root 0=0 and taking log to the base 10. The conversation ends with one member stating that the discussion is a proof method learned at IIT Delhi.
  • #1
ritwik06
580
0

Homework Statement


[tex]0^{\sqrt{0}}=\sqrt{0^{0}}[/tex]

Is this expression true?
 
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  • #2


If you consider "undefined = undefined" to be true, then yes.
 
  • #3


That depends on your view... 0^0 can be defined as 1, or it can be undefined.

See http://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_zero_powerEither way, I think if you define 0^0 as undefined then the expression above does not hold... That would also mean 1/0 = 0^0 which I think doesn't really make sense... I'm not sure on this but I don't think you can say undefined = undefined!
 
  • #4


Take logarithm and simplify.

root 0 * log 0 = 0 *1= 0

Assumptions= using root 0= 0 on the basis that zero is a real number.
Taking log to the base 10.

R.H.S.> 1/2*0 * log 0
> 0*1
> 0

Assumptions same as above.

The points raised above by honourable members are very meaningful, this is one of the proof methods i learned at the IIT,delhi.
 
  • #5


physixguru said:
Take logarithm and simplify.

root 0 * log 0 = 0 *1= 0
?? log(0) is NOT 1. It is, one more time, "undefined".
(log(1)= 0, not the other way around.)

Assumptions= using root 0= 0 on the basis that zero is a real number.
Taking log to the base 10.

R.H.S.> 1/2*0 * log 0
> 0*1
> 0

Assumptions same as above.

The points raised above by honourable members are very meaningful, this is one of the proof methods i learned at the IIT,delhi.
 
  • #6


It was a bad typing error.
 

What is an exponent expression?

An exponent expression is a mathematical expression that represents repeated multiplication of a number by itself. It is written in the form of a base number raised to a power, such as 3^2, where 3 is the base and 2 is the power.

What is the difference between an exponent and a base number?

The base number is the number that is being multiplied by itself, while the exponent is the number that represents how many times the base number is being multiplied. For example, in the expression 4^3, 4 is the base and 3 is the exponent.

How do I simplify an exponent expression?

To simplify an exponent expression, you can use the rules of exponents. For example, when multiplying two exponent expressions with the same base, you can add the exponents together. When dividing two exponent expressions with the same base, you can subtract the exponents.

What is the meaning of a negative exponent?

A negative exponent means that the base number should be divided by itself the number of times indicated by the exponent. For example, 2^-3 is the same as 1 / (2^3), which equals 1/8.

How can I evaluate an exponent expression with variables?

To evaluate an exponent expression with variables, you can substitute in the given values for the variables and then use the rules of exponents to simplify the expression. You can also use a calculator to evaluate the expression if the variables have specific numerical values.

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